\fdO'^ - Old Forge Coal Mines

a^j^ac-\-^
ALGEBRA. Ill
a" - "lac {- c" - U"
a" - lab + ^' - c' a'c - ac*
which, being placed in parentheses, become
a" J^ac-\-c^ {a' - 2ac + c') - ^
{a' - 2ad -\- d')- c' a*c - ac*
By Art. 456, we know that «" — 2ad + ^', also a" — 2ac
-\- c^, are perfect squares, and may be written {a — by and
{a-c)\
Factoring a*c — ac* by Case I, Art. 452, we have
a^ ^acJ^ c" {a - c)' - b"" _
(rt _ by -c'^ ac ~
{a' -c')
a' -{• ac -\- c' {a — c — b) {a — c -\- b)
{a — b— c) {a -^b -\- c) ac {a — c) (a" -\- ac -\- c')'
(Arts. 463 and 466.)
Canceling common factors and multiplying, we have
a — c -\- b a-\- b — c .
or —; ;!—— ^-, r. Ans.
{a — b -{- c) ac {a — cy ac {a — b -\- c) {a — cy
(212) The square root of the fraction a plus b plus c
divided by n, plus the square root of a, plus the fraction b
plus c divided by 7i, plus the square root of a plus b, plus
the fraction c divided by «, plus the quantity a plus b, into
c, plus a plus be.
(213) {a)-^ 5:r- + i2P-
We will first reduce the fractions to a common denomina-
tor. The L. C. M. of the denominator is 60-r', since this is
the smallest quantity that each denominator will divide
without a remainder. Dividing 00,1'" by 3, the first denom-
the second
inator, the quotient is 20;r' ; dividing GO;r' by 5x,
denominator, the quotient is 12x; dividing GO;ir' by 12x', the
third denominator, the quotient is 5. Multiplying the corresponding
numerators by these respective quotients, we
obtain 20^'(4;r + 5) for the first new numerator — ; V2x{3x 7)
for the second new numerator, and 5 X 9 = 45 for the third
new numerator. Placing these new numerators over the
common denominator and expanding the terms, we have